Do you have a reasonable number of percentiles per variable, say, the 1%, 2%, 3%... 99% percentiles (or at least in 5%-steps)? It must be enough to be able to reconstruct the approximate distribution.

From this information you can built a frequency table for grouped data:

If the 10%-percentile is x and the 15%-percentile is y, then there are (15-10)=5% of the values >x and

Dear Mohan, The best method would be to write to the authors of the original papers and to request these data from the original databases.

Thank you very much for your answers. But in my case I only have the 25%, 50% and 75% values with the highest and lowest values observed. If I use the above method, will the results greatly deviate from the correct answer?

Since you have the highest and lowest values, the range rule tells us that the standard deviation of a sample is approximately equal to one fourth of the range of the data [i.e., SD = (Maximum – Minimum)/4].

The relationship between mean, median and mode is as follows:

Mean – Mode = 3(Mean – Median).

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Article Estimating the sample mean and standard deviation from the s...

The formula

Mean – Mode = 3(Mean – Median).

regarding the relationship between mean, median and mode is correct.

However, this relationship is an empirical one (due to Kearl Pearson) but not a theoretical one.

Therefore, it can not give the exact value but an approximate value.

On the other hand, I have little doubt on the formula/theorem

"the standard deviation of a sample is approximately equal to one fourth of the range of the data [i.e., SD = (Maximum – Minimum)/4]"

as mentioned by Kandasamy Ravichandran.

Kandasamy Ravichandran is requested to give some reference related to the theorem.